12.1.0.2: Upgrade failing due to edition problems

While the MOS article "Database Upgrade to 12.1.0.2 Fails with Error: “ORA-38802: edition does not exist”" has a pretty clear title, note ID 1995415.1 does not have a whole lot of details beyond the bug and that there is a patch associated to fixing this.  Well looking at the bug has the details we are looking for since it seems like several objects, especially ORA$BASE, have no edition information so the installer is crashing!